Method for estimating the time of arrival in ultra wideband systems

ABSTRACT

Method and device for estimating the time-of-arrival of a received signal y(t), said method comprising the step of: generating a plurality of frequency-domain samples from the received signal y(t); estimating a correlation matrix (Formula I) from said plurality of frequency-domain samples; from said correlation matrix (Formula I), calculating a signal energy distribution with respect to different propagation delays; finding a delay value (Formula II) at which said signal energy distribution exceeds a certain threshold P th , said delay value representing the time-of-arrival estimation.

FIELD OF THE INVENTION

The present invention relates to the estimation of the time-of-arrival(ToA) of signals transmitted through a wireless medium. More precisely,the present invention relates to the estimation of the ToA of signals inultra wideband (UWB) systems.

STATE OF THE ART

Communication systems based on impulse radio ultra wideband (IR-UWB)have been envisaged as radio communication systems that could enablevery accurate ranging and location applications, given the extremelyshort duration pulses. This high time resolution nature of the UWBsignal makes ToA estimation method a good candidate for positioningestimation in UWB communications.

Time-based positioning techniques rely on measurements of thepropagation time undertaken by the signal when travelling between atarget node and a reference node. This typically requires a minimum ofthree reference nodes to estimate the position in a two-dimensionalspace.

For ranging applications a single reference node is sufficient. Rangingaccuracy depends on how precisely the receiver can discriminate thefirst arriving signal, which in a multipath environment may not be thestrongest. Currently, most of the known ranging techniques are based ontime-domain ToA estimation methods. The maximum likelihood (ML) solutionhas practical limitations due to the requirement of very high samplingrates. The conventional correlation-based approach described by V.Somayazulu, J. R. Foerster and S. Roy [“Design challenges for very highdata rate uwb systems”, in Asilomar Conference on Signals, Systems andComputers] results in a very slow TOA estimator requiring an exhaustivesearch over a large number of bins. Iterative ML approaches have alsobeen studied by J. Y. Lee and R. Scholtz [“Ranging in dense multipathenvironment using uwb radio links”, IEEE J. Selected Areas Commun., vol.20, no 9, December 2002], but yet requiring very high rate sampling.

Recently, proposals to reduce the sampling constraints and timeintervals required for estimation of time-domain based ToA estimatorshave appeared in the literature. An approach addressed by S. Gezici, Z.Sahinoglu, A. Molisch, H. Kobayashi and V. Poor [“A Two-Step ToAEstimation Algorithm for Impulse Radio UWB Systems, Mitsubishi ElectricResearch Laboratories, December 2005] consists on a two step ToAestimation process consisting of an initial coarse estimation of the ToAfollowed by a higher resolution stage. Following this strategy, a firstrough ToA estimate based on the received signal energy is followed by alow-rate correlation stage that estimates the ToA based on hypothesistesting. A similar two-step estimator is proposed by I. Guvenc and Z.Sahinoglu [“Threshold-based ToA estimation for impulse radio uwbsystems”, IEEE International Conference on Ultra-wideband], based on athreshold-based energy detection receiver. The scheme allows for asymbol rate sampling but requires using several symbols and anappropriate design of the signal waveform. A further two stage approachis considered by P. Cheong, A. Rabbachin, J. Montillet, K. Yu and I.Oppermann [“Synchronization, toa and position estimation forlow-complexity ldr uwb devices”, IEEE International Conference onUltra-Wideband], who describes a non-coherent receiver based on anenergy detection stage, based on integration windows which timeresolution changes between the two stages. A critical parameter forthese estimators lies on the threshold selection.

In summary, most of the known techniques on ranging applications in UWBcommunications systems are based on time domain techniques fortime-of-arrival estimation. However, time domain approaches suffermainly from (a) practical limitations of maximum likelihood solution dueto the requirement of very high sampling rates and (b) large estimationtime of correlation-based approaches due to the required search over alarge number of bins.

SUMMARY OF THE INVENTION

It is therefore an object of the present invention to provide a methodfor the time-of-arrival (ToA) estimation of a signal transmitted througha wireless system which is based on a frequency domain approach. Thisallows sub-Nyquist sampling rates while achieving high ranging accuracy.Thus, the time-of-arrival is estimated from the frequency domain sampledsignal. Therefore, this low complexity ToA estimation method solves theproblems derived from known ToA estimation methods.

In particular, it is an object of the present invention a method forestimating a time-of-arrival of a received signal y(t), said methodcomprising the step of: generating a plurality of frequency-domainsamples from the received signal y(t); estimating (41) a correlationmatrix {tilde over (R)}_(YY) from said plurality of frequency-domainsamples; from said correlation matrix {tilde over (R)}_(YY), calculatinga signal energy distribution with respect to different propagationdelays; finding a delay value at which said signal energy distributionexceeds a certain threshold P_(th), said delay value representing thetime-of-arrival estimation.

Said received signal is preferably an ultra-wideband signal, and mostpreferably an impulse radio ultra-wideband signal. In this case, thestep of estimating a correlation matrix from a plurality offrequency-domain samples is carried out by means of exploiting thetemporal diversity of said impulse radio ultra-wideband signal.

Said signal energy distribution is preferably given by the computationof a pseudo-periodogram.

Said step of finding said delay value can be done by exhaustivelyevaluating the signal energy distribution at a plurality of values ofthe propagation delay.

Alternatively, said step of finding said delay value is done bycalculating the roots of a polynomial.

The step of generating a plurality of frequency-domain samples from thereceived signal y(t) is preferably done by: splitting the receivedsignal y(t) into a plurality of bands by filtering said received signalby band-pass filters with approximately Gaussian frequency response;sampling the output of each of the band-pass filters thereby obtaining aplurality of samples; from said plurality of samples, building a vectorS; from said vector S, creating a vector S′; creating a vector Y whichis the concatenation of vector S, a vector of zeros of size Q, where Q≧1and vector S′.

It is another object of the present invention to provide a device forestimating the time-of-arrival (ToA) of a signal transmitted through awireless system, which comprises means adapted for carrying out thesteps of the method for the time-of-arrival (ToA) estimation. Inparticular, the device for ToA estimation is preferably based on UWBreceiver architectures that provide direct samples of the receivedsignal in the frequency domain at sub-Nyquist sampling rate.

Finally, it is a further object of the present invention to provide acomputer program.

The advantages of the proposed invention will become apparent in thedescription that follows.

BRIEF DESCRIPTION OF THE DRAWINGS

To complete the description and in order to provide for a betterunderstanding of the invention, a set of drawings is provided. Saiddrawings form an integral part of the description and illustrate apreferred embodiment of the invention, which should not be interpretedas restricting the scope of the invention, but just as an example of howthe invention can be embodied. The drawings comprise the followingfigures:

FIG. 1A shows a block diagram of a frequency-domain sampling (FDS)receiver (10) according to an embodiment of the present invention.

FIG. 1B shows a block diagram of a frequency-domain sampling (FDS)receiver (10′) according to an embodiment of the present invention.

FIG. 2 shows a block diagram of a frequency-domain sampling (FDS)receiver (20) according to a preferred embodiment of the presentinvention.

FIG. 3 shows an example of a particular implementation of the receiveraccording to the preferred embodiment of the present invention.

FIG. 4 shows some frequency domain sampling examples.

FIG. 5A shows a block diagram of the digital section of a receiveraccording to an embodiment of the present invention.

FIG. 5B shows a block diagram of the digital section of a receiveraccording to an embodiment of the present invention.

FIG. 6A shows a ToA estimation scheme according to an embodiment of thepresent invention.

FIG. 6B shows a ToA estimation scheme according to an embodiment of thepresent invention.

FIG. 7 shows some blocks of the ToA estimation scheme according to anembodiment of the present invention.

FIG. 8 shows a ToA estimation scheme according to a further embodimentof the present invention.

FIG. 9 shows the signal samples obtained at the output of the ADC stage.

DETAILED DESCRIPTION OF THE INVENTION Definitions

In the context of the present invention, the term “approximately” andterms of its family (such as “approximate”, “approximation”, etc.)should be understood as indicating values or forms very near to thosewhich accompany the aforementioned term. That is to say, a deviationwithin reasonable limits from an exact value or form should be accepted,because the expert in the technique will understand that such adeviation from the values or forms indicated is inevitable clue tomeasurement inaccuracies, etc. The same applies to the term “nearly” and“Gaussian-like”.

Furthermore, the term “pseudo” has been employed accompanying terms suchas “spectrum” or “periodogram”. Thus, the expressions “pseudo-spectrum”and “pseudo-periodogram” are used. The term “pseudo” is used because theterms “spectrum” and “periodogram” are normally used in the frequencydomain. For example, the “spectrum” normally denotes de distribution ofenergy in the frequency domain. However, in the context of the presentinvention, we refer to “spectra” and “periodograms” in the temporaldomain, more precisely, in the domain of temporal delays In order toemphasize the use of these terms in a domain which is not the typicalone for said terms, we have employed the term “pseudo”.

In this text, the term “comprises” and its derivations (such as“comprising”, etc.) should not be understood in an excluding sense, thatis, these terms should not be interpreted as excluding the possibilitythat what is described and defined may include further elements, steps,etc.

Signal Model

Although this invention is not limited to the particular structure ofimpulse radio (IR) ultra wideband (UWB) signals, next a signal model ofIP-UWB signals is introduced.

Ultra wideband signals based on impulse radio (IR) transmission consistof baseband impulses of very short duration, typically of about 100picoseconds. A single information symbol is typically implemented by therepetition of N_(p) pulses of very short duration,

$\begin{matrix}{{s(t)} = {\sum\limits_{p = 0}^{N_{p} - 1}{\sqrt{E_{p}}{p\left( {t - {pT}_{pr}} \right)}}}} & (1)\end{matrix}$where E_(p) denotes the pulse energy, p(t) refers to the single pulsewaveform, typically a Gaussian monocycle or its derivatives and T_(pr)is the repetition pulse period.

Modulation and time hopping can be explicitly included in the pulsewaveform such us p(t)=p_(s)(t−b_(i)T_(Δ)−c_(i) ^(p)T_(c)) with p_(s)(t)being typically a Gaussian monocycle or its derivatives, b_(i) theinformation symbol, T_(Δ) the modulation time shift, c_(i) ^(p) the timehopping sequence and T_(i) the chip interval.

Assuming that the channel is modelled by a summation of impulses (DiracDelta function), the received signal y(t) through a multipath fadingchannel is a sum of multiple delayed and attenuated replicas of thetransmitted signal s(t), where h_(m) and τ_(m) respectively denote thefading coefficient and the delay for the m-th path and v(t) is thecontribution of the additive Gaussian noise:

$\begin{matrix}{{y(t)} = {{\sum\limits_{p = 0}^{N_{p} - 1}{\sum\limits_{m = 1}^{M}{h_{m}\sqrt{E_{p}}{p\left( {t - {pT}_{pr} - \tau_{m}} \right)}}}} + {v(t)}}} & (2)\end{matrix}$

Transforming the signal to the frequency domain,

$\begin{matrix}{{Y(\omega)} = {{\sum\limits_{p = 0}^{N_{p} - 1}{\sum\limits_{m = 1}^{M}{h_{m}\sqrt{E_{p}}{P(\omega)}{\mathbb{e}}^{{- j}\;\omega\;{pT}_{pr}}{\mathbb{e}}^{- {j\omega\tau}_{m}}}}} + {V(\omega)}}} & (3)\end{matrix}$where Y(ω), P(ω) and V(ω) denote the Fourier transform of respectivelythe received signal, the transmitted pulse and the additive Gaussiannoise.

Rearranging this formula into matrix notation, the sampled receivedsignal can be written as

$\begin{matrix}{Y = {{\sqrt{E_{p}}{\sum\limits_{p = 0}^{N_{p} - 1}{P_{p}E_{\tau}h}}} + V}} & (4)\end{matrix}$where:

-   -   the elements of vector YεC^(K×1), Y(ω_(k)), are the discrete        Fourier transform (DFT) components of y(t) with ω_(k)=kω₀ for        k=0,1, . . . ,K−1 and ω₀=2π/K;    -   P_(p) is a diagonal K×K matrix (same size as DFT) that contains        the DFT components of the pulse waveform p(t) shifted by a        frequency factor e^(−jωpT) ^(pr) ;    -   h=[h₁ . . . h_(M)]^(T) is the fading coefficients vector having        M×1 size. “T” denotes the “transpose matrix”. Each element of        this vector is, in general, a complex number which represents        the channel attenuation associated to the multipath.    -   VεC^(K×1) is the noise vector, wherein C denotes that its        elements are complex numbers; its size is K×1; and    -   E_(τ) is a K×M matrix, which denotes the delay-signatures for        each delayed signal:    -   E_(τ)=[e_(τ) ₁ . . . e_(τj) . . . e_(τ) _(M) ], with column        vectors e_(τ) _(j) =[1 e^(−jω) ⁰ ^(τ) ^(j) . . . e^(−jω) ⁰        ^((K−1)τ) ^(j) ]^(T). K is the size of the DFT and M is the        number of multipaths which are taken into account.

Description of the Receiver

FIG. 10A shows a block diagram of a frequency domain sampling (FPS)receiver (10) according to the present invention. Receiver (10)comprises a receiving antenna (11) followed by an amplifier, typically awideband low noise amplifier (LNA) (12). After said amplifier (12), aradio frequency (RE) front-end (13) is located, followed by a digitalsignal processing unit (DSPU) (19). The radio frequency (RE) front-end(13) provides the digital signal processing unit (DSPU) (19) with a setof samples in the frequency domain (Y(0), Y(1), . . . , Y(K−1)).

Since one of the objects of the present invention is a method forestimating the time of arrival of a signal transmitted through awireless medium, based on a receiver which provides direct samples ofthe received signal in the frequency domain, any radio frequency (RF)front-end (13) which is able to provide the digital signal processingunit (19) with a set of samples in the frequency domain (Y(0), Y(1), . .. , Y(K−1)) can be used.

If the RF front end provides a signal in the time domain, anintermediate stage performing the Discrete Fourier Transform of suchsignal is necessary. A block diagram of such a receiver (10′) is shownin FIG. 1-B, where reference 15 refers to any RE front-end providing atime domain digital signal and reference 16 refers to a digital blockperforming the Discrete Fourier Transform.

FIG. 2 shows a block diagram of a frequency-domain sampling (FDS)receiver (20) according to a preferred embodiment of the presentinvention. The FDS receiver (20) of FIG. 2 samples, at Nyquist rate, thesignal only in the frequency bands of interest. A receiver in the timedomain must sample the entire signal at Nyquist rate, which results in ahigher overall sampling rate. Therefore, this preferred embodimentrequires lower sampling clock frequencies than time-domain sampling(TDS) receivers. Similar to receiver (10) or (10′), receiver (20)comprises a receiving antenna (21), an amplifier, typically a widebandlow noise amplifier (LNA) (22), followed by a radio frequency (RE)front-end (23) which, in turn, is followed by a digital signalprocessing unit (DSPU) (29).

In this preferred embodiment of the present invention, the RE front-end(23) comprises a power splitter (PS) (220), a filter bank (25-1, 25-2, .. . , 25-N) and an analog-to-digital (ADC) conversion stage (28-1, 28-2,. . . , 28-N). The power splitter (220) splits the received signal intoN branches. Each of said branches enters one of the filter banksbandpass filters (25-1, 25-2, . . . , 25-N), which delivers the signalfiltered at the corresponding sub-band. As a result, the filter bankdecomposes the received signal into N equally spaced, nearly orthogonalfrequency bands representing the spectral components of the receivedsignal. The frequency domain decomposition is based in the discreteShort Time Fourier Transform (STFT), which can decompose a signal in anorthogonal basis.

The discrete STFT of a signal x(t) is defined as:

S T F T(n, m) = ∫_(−∞)^(∞)x(t)γ_(n ⋅ m)^(*) (t)𝕕twhere γn,m(t) are the STFT basis functions. Typically, the STET basisfunctions consist of a window function translated in both time andfrequency. By properly choosing the window function and translationintervals, a set of orthogonal frequency bands can be obtained. In thedescribed receiver implementation, γ_(n,m)(t) corresponds to the n^(th)band filter, delayed by m times the sampling period. In order to obtainthe STET coefficients, STFT(n,m), one must sample each filter output attime intervals spaced by m times the sampling period. This operation isperformed by the analog-to-digital (ADC) conversion stage (28-1, 28-2, .. . , 28-N), which samples the measured spectral components delivered bythe filter bank (25-1, 25-2, . . . , 25-N).

Finally, a digital signal processing unit (DSPU) (29), which will bedescribed in detail later, performs signal detection, synchronizationand channel equalization in the frequency domain.

The receiver can be designed with any number of filters in the filterbank (25-1, 25-2, . . . , 25-N), provided that a physical implementationis feasible. The number of filters in the filter bank determines thedimension of the ToA estimator, since it determines the dimension ofvector S, which will be introduced later in this description. Inaddition, since the signal bandwidth is constant, the number of filtersdetermines the filter bandwidth, which in turn determines the samplingrate of the ADC stages (28-1, 28-2, . . . , 28-N). Nevertheless, theoverall sampling rate at which the receiver (20) operates remainsconstant, since it is given by the sum of the sampling rates of all ADCstages (28-1, 28-2, . . . , 28-N).

In a system with a signal bandwidth of W, the frequency spacing Δfbetween the N filters (25-1, 25-2, . . . , 25-N) is given by:

$\begin{matrix}{{\Delta\; f} = \frac{W}{N - 1}} & (5)\end{matrix}$

Each filter (25-1, 25-2, . . . , 25-N) measures one in-band spectralcomponent during an interval of T_(a)=1/Δf (sampling period). The ADCconversion stage (28-1, 28-2, . . . , 28-N) samples the filter outputsat a rate F_(m)=1/T_(a) (sampling frequency) to avoid time-domainaliasing. The observation samples after the ADC conversion operation arethe N spectral components of the received signal, which are grouped in avector S=[S(0) . . . S(N−1)]^(T) of size 1×N, and wherein “T” denotes“transpose matrix”. Given the symmetry of the discrete time Fouriertransform of signal y(t), an estimated K-length frequency response isformed by appending the observation frequency samples of vector S withthemselves in reversed order and zero padding at the extreme and centralsampled positions, as follows:Y=[0 . . . 0 S^(T) 0 . . . 0 S′^(T) 0 . . . 0]^(T)   (6)where S′=[S(N−1) . . . S(0)]^(T). The minimum number of measuredspectral components in the frequency-domain sampling (FDS) approach isgiven by:N=┌W T _(a)+1┐  (7)

FIG. 4 shows some frequency domain sampling examples:

FIG. 4( a) shows the analogical, frequency domain spectrum of a signalr(t). In the ordinates axis the frequency response R(f) is represented,while in the abcisses axis the frequency domain f_(Δ) is represented.

FIG. 4( b) shows the discrete-time frequency response Rs(m) of the samesignal (after time sampling of the received signal and performing aDiscrete Fourier Transform (DFT). Abcisses axis represents the values ofthe discrete frequency ω, wherein ω=2π/K. Rs(m) is a periodic signal.

FIG. 4( c) shows the estimated discrete time signal in the time domain,after performing an Inverse Discrete Fourier transform (IDF). Ordinatesaxis represents the temporal signal r(n) and abcisses axis representsthe temporal samples (n).

As explained before, any radio frequency (RF) front-end (13, 23) whichis able to provide the digital signal processing unit (19, 29) with aset of samples in the frequency domain can be used. However, using a RFfront-end (23) based on an analog stage which comprises a filter bank(25-1, 25-2, . . . , 25-N) like the one which has just been proposed(FIG. 2) provides the advantage of incurring in lower complexity ofimplementation, since the ADC conversion stages (28-1, 28-2, . . . ,28-N) need a lower sampling frequency. A second advantage of thisapproach lies on the fact that this RF front-end directly provides thefrequency samples which are needed for the ToA estimation, withoutrequiring a time to frequency conversion.

As a way of example, which must not be considered as a limitation of thepresent invention, FIG. 3 shows a possible implementation of thereceiver (30) according to this preferred embodiment, capable ofsampling an impulse radio ultra wideband (IR UWB) signal. The receiver(30) comprises a receiving antenna (31), a wideband low noise amplifier(32) and a RF front-end (33). This RF front-end (33) comprises a powersplitter PS (320), a second amplifier stage (34-1, 34-2, . . . , 34-4),a band of band-pass filters (35-1, 35-2, . . . , 35-4), a downconversion stage for in-phase and quadrature signals (36-1, 36-2, . . ., 36-4), a third amplifier stage (37-1, 37-2, . . . , 37-4), whichcomprises variable gain amplifiers (VGA) with automatic gain control(AGC) input and an analog-to-digital (ADC) conversion stage (38-1, 38-2,. . . , 38-4). The digital signal processing unit (DSPU) which followsthe ADC conversion stage is not represented in FIG. 3. The receiver (30)can implement a nearly orthogonal, discrete STFT as defined earlier. Thediscrete STFT coefficients are obtained by periodically sampling theoutput of each filter. The 4 bandpass filters shown (35-1, 35-2, . . . ,35-4) are designed with a Gaussian-lice frequency response, wherein eachfilter has a bandwidth of approximately 500 MHz approximately centeredat the following frequencies f₀, f₁=f₀+1 GHz, f₂=f₁+1 GHz, and f₃=f₂+1GHz. As a result, the basis is nearly orthogonal and does therefore notrequire phase synchronization of all filters, which is hard to obtain inpractice. Also as a way of example, the sampling rate of the ADCconversion stage can be chosen to be 1 Gigasample per second, i.e.,Nyquist rate. The digital signal processing unit (DSPU) processes the 4channels to reconstruct the received signal and implements the signaldetection and time-of-arrival estimation algorithms, as will beexplained later in this description.

Description of the Digital Section of the Receiver

FIGS. 5-A and 5-B show a block diagram of a possible implementation ofthe digital signal processing unit (DSPU) (19, 29) of the receiver (10,10′, 20, 30). The only difference between the DSPU (19) (FIG. 5-A) andthe DSPU (29) (FIG. 5-B) is that the first one (19) corresponds to areceiver (10, 10′) whose REF front-end (13) provides at its output a setof K samples in the frequency domain (Y(0), Y(1), . . . , Y(K−1)), whilethe second one (29) corresponds to a receiver (20, 30) whose RFfront-end (23, 33) provides at its output a set of N samples in thefrequency domain (S(0), S(1), . . . , S(N−1)), wherein K>2N (seeequation (6)). In other words, DSPU (29) (FIG. 5-B) takes advantage of aradio frequency front end (23, 33) which incurs in lower complexity ofimplementation than the other one (13), as already explained. The DSPU(19, 29) comprises the following functional blocks:

-   -   means (40, 40′) for estimating the time-of-arrival (ToA), which        carries out a ToA estimation algorithm for obtaining the time        delay of the received signal with respect to a local time basis.        The estimated time delay, which is performed in the transformed        domain, yields a ranging estimate and is used, among others, for        timing acquisition to synchronize the receiver (10, 10′, 20,        30);    -   means (50) for estimating the channel, which carries out channel        estimation algorithms. The estimated channel response        corresponds to the combination of the channel impulse response        and the transmitting and receiving antennae distortion. This        means (50) obtains the coefficients corresponding to a matched        filter of the receiver;    -   a matched filter (60), which multiplies the received signal        vector with the conjugate of the estimated channel impulse        response. The multiplication is performed in the transform        domain. In addition, the matched filter (60) also combines the        multiple received pulses according to the time-hopping sequence.        Its output is a symbol-rate signal;    -   a time hopping (TH) sequence generator (70), which obtains the        time-hopping sequence used to modulate the transmitted pulses;    -   means (80) for implementing demodulating and decoding algorithms        in order to obtain the information bits from the output of the        matched filter (60).

In the following section, the means (40) and method for ToA estimationaccording to the present invention is described in detail.

Time-of-Arrival (ToA) Estimation

In this section, the method for ToA estimation according to the presentinvention is described. Its application is intended for use at severalprocessing blocks in the receiver (10, 10′, 20, 30), such as rangingestimation, positioning location and timing synchronization.

The receiver architecture has a significant impact in the choice of theranging technique. The estimation problem resorts then to estimate theToA from the frequency domain sampled signal as delivered from the radiofrequency front end (13, 23, 33). As already explained, depending on thearchitecture of the RF front end (13, 23, 33), a reduced set of samples(S(0), S(1), . . . , S(N−1)) is obtained (FIGS. 2, 3) or a complete setof K samples (Y(1),Y(1), . . . ,Y(K−1)) is obtained.

According to an embodiment of the present invention, represented in FIG.5-A, a vector Y is directly formed from the K samples delivered from theradio frequency front end (13). As shown in FIG. 5-A, this vector Y isthe input of block 40, which is the block responsible for the time ofarrival estimation. Block 40 is detailed in FIG. 6-A.

According to another embodiment of the present invention, in which theradiofrequency front-end (23, 33) provides a reduced set of samples(S(0), S(1), . . . , S(N−1)) (FIGS. 2, 3), a vector S=[S(0) . . .S(N−1)] is the input; of block 40′ (FIG. 5-B) Block 40′ is detailed inFIG. 6-B, which differs from FIG. 6-A in that a block 39 is needed forcreating a vector Y (formed by K elements). In a particular embodiment,vector Y comprises 2N+1 elements. The outputs of the N ADC (28-1, . . ., 28-N; 38-1, . . . , 38-N) form a vector S=[S(0) . . . S(N−1)]. If avector S′ is created, such as S′=[S(N−1) . . . S(0)], then vector Y:Y=[S 0 S′]^(T) comprises K=2N+1 elements, K being the size of the FFT.By zero padding the size of the DFT can be increased, thereby obtaininga higher value of K, as previously shown in equation (6).

The estimation algorithm according to the present invention is based onthe definition of the pseudo-spectrum as the signal energy distributionwith respect to propagation delays (temporal delays). The temporalpseudo-spectrum amplitude at each time or propagation delay can beobtained by estimating the energy of the signal filtered by thedelay-signature vector at said time delay defined as e_(τ)=[1 e^(−jω)^(o) ^(τ) . . . e^(−jω) ⁰ ^((K−1)τ)]^(T). Then, the pseudo-spectrumyields the quadratic form e_(τ) ^(H)R_(YY)e_(τ) defined aspseudo-periodogram, wherein R_(YY) is the correlation matrix defined asR_(YY)=E[YY^(H)], where E[.] denotes the expected value.

The estimation algorithm comprises the following steps: estimation ofthe correlation matrix, denoted as {tilde over (R)}_(YY), from thefrequency domain samples (Y(0),Y(1), . . . ,Y(K−1)); calculation of atemporal pseudo-spectrum P(τ) from said estimated correlation matrix;finding a delay value ({tilde over (τ)}₀) that exceeds a given thresholdin the temporal pseudo-spectrum.

FIGS. 6-A and 6-B show a ToA estimation scheme (40, 40′) according tothe present invention. Once obtained vector Y, the ToA estimation methodcomprises a first stage (41) for estimating the correlation matrix{tilde over (R)}_(YY) and a second stage (42) for calculating the ToA.

In the first stage (41), the correlation matrix of the sampled signal inthe frequency domain (Y(0),Y(1), . . . ,Y(K−1)) is calculated from theobservations of the received signal.

Considering that a plurality of N_(s) signal realizations are observed(for instance, one signal realization may be the transmission of onedata symbol of T_(s) seconds), the correlation matrix corresponding toeach sampling interval of T_(a) seconds can be estimated averaging theobservation vectors corresponding to said sampling interval over theN_(s) realizations. For each sampling interval n, a plurality of N_(s)observation vectors (Y_(1,n) Y_(2,n) . . . Y_(N,n)) can be defineddenoting Y_(s,n)=[Y_(s,n)(0) Y_(s,n)(1) . . . Y_(s,n) (K−1)]^(T) as theobservation vector corresponding to the s-th realization, at samplinginterval n, which composed of the K frequency samples. This isillustrated in FIG. 9. From said plurality of observation vectors, thecorrelation matrix is estimated for each sampling interval n:

${{\overset{\sim}{R}}_{YY}(n)} = {\frac{1}{N}{\sum\limits_{s = 1}^{N_{s}}{Y_{s \cdot n}Y_{s \cdot n}^{H}}}}$

Following the stage (41) at which the correlation matrix of the sampledsignal in the frequency domain (Y(0),Y(1), . . . ,Y(K−1)) is obtained,there is a second stage (42) in which ToA is calculated. FIG. 7 shows indetail the second stage (42′) for calculating the ToA:

Firstly, calculation of a temporal pseudo-spectrum from said correlationmatrix {tilde over (R)}_(YY) is carried out (421).

In a preferred embodiment of the present invention, but not limitedthereto, the temporal pseudo-spectrum (421) proposed for the estimationof the ToA can be obtained by means of the calculation of a temporalpseudo-periodogram, which is defined as follows:P _(n)(τ)=e _(τ) ^(H) {tilde over (R)} _(YY)(n)e _(τ)  (8)where {tilde over (R)}_(YY)(n) denotes the correlation matrix of thesampled signal in the frequency domain corresponding to the n-th sampleinterval, e_(τ)=[1 e^(−jω) ⁰ ^(τ) . . . e^(−jω) ⁰ ^((K−1)τ)]^(T) denotesa delay-signature vector, and wherein ω₀ is 2π/K, τ is the temporaldelay and K is the number of frequency samples at each observationvector

Secondly, a delay value ({tilde over (τ)}₀) that exceeds a giventhreshold in the temporal pseudo-spectrum is calculated (422). Saidthreshold P_(th) is estimated (obtained empirically).

The algorithm for searching said delay value ({tilde over (τ)}₀) is asfollows: A pseudo-periodogram P(τ) is built, which is a function thatcan be evaluated at different temporal values of τ and at differentsample intervals n. Depending on the desired resolution or on thecomputational load desired, a certain amount of values of τ is selected.Starting with the first sample interval, n=1, the pseudo-periodogramP_(n)(τ) is calculated and the first τ=τ₀ for which the value ofP_(n)(τ₀) is over a certain threshold P_(th) is searched. Said value ofτ=τ₀ for which P_(n)(τ₀))>P_(th) is the estimated delay {tilde over(τ)}₀, and therefore the ranging estimate (by simply multiplying {tildeover (τ)}₀ by the propagation speed) is directly obtained. If no valueof τ exceeding the threshold P_(th) is found, the algorithm continueswith the next sample interval and repeats the process. The threshold,P_(th), depends on particular scenarios and is dependent on the noisepower at the receiver.

Next, the ToA estimation algorithm of the present invention is appliedfor the estimation of the time of arrival of impulse radio ultrawideband signals (IR-UWB). Thus, it is shown how the algorithm exploitsthe temporal diversity inherent to IR-UWB signals, which transmit N_(p)pulses with a repetition period of T_(pr) (equations (1) to (3)). Thisis shown in FIG. 8.

The temporal diversity (repetition of each pulse N_(p) times) is usedfor the estimation of the correlation matrix in IR-UWB. For each one ofthe N_(p) repeated pulses which are transmitted in an IR signal (seeequation (1)), a vector with the corresponding K frequency samplesY_(s,n) is built. This vector is similar to the one already describedwhen the first stage (41) of the ToA estimation scheme was presented.Since each IR signal transmits N_(p) repeated pulses, N_(p) frequencyvectors (observation vectors) Y_(s,n) ⁽¹⁾ . . . Y_(s,n) ^((N) ^(p) ⁾ canbe built. With these N_(p) frequency vectors Y_(s,n) ⁽¹⁾ . . . Y_(s,n)^((N) ^(p) ⁾ a diversity matrix Z_(s,n) is conformed:Z _(s,n) =[Y _(s,n) ⁽¹⁾ . . . Y _(s,n) ^((N) ^(p) ⁾]wherein Y_(s,n) ^((p)) denotes the frequency components associated toreceived pulse p at realization s and sample interval n and wherein p isa natural number which goes from 1 to N_(p).

From this diversity matrix Z_(s,n) the correlation matrix {tilde over(R)}_(YY)(n) is estimated by,

${{\overset{\sim}{R}}_{YY}(n)} = {\frac{1}{N_{s}}{\sum\limits_{s = 1}^{N_{s}}{Z_{s \cdot n}Z_{s \cdot n}^{H}}}}$

The exploitation of the temporal diversity of impulse radio ultrawideband signals (IR-UWB) lies therefore in taking into account theobservations of N_(p) received repeated pulses when building theobservation, said matrix Z_(s,n), from which a correlation matrix {tildeover (R)}_(YY)(n) is calculated.

Now, coming back to the temporal pseudo-spectrum obtained by means of apseudo-periodogram as defined in equation (8), instead of evaluating thepseudo-spectrum (8) at each point over which the search is performed,the invention provides, in a further embodiment, an alternativealgorithm, denoted as root-periodogram, which finds the roots of apolynomial, thus reducing the search over a few points. Note that boththe previous algorithm and this alternative algorithm can be appliedindependently from the nature of the received signal, since bothalgorithms are calculated from the correlation matrix {tilde over(R)}_(YY)(H) (independently from the way of obtaining this correlationmatrix).

The root-periodogram comprises the following steps: calculating aperiodogram from the received samples; calculating the roots of apolynomial; selecting a root for that polynomial, said rootcorresponding to a maximum which is over a previously determinedthreshold.

The idea is therefore to find the maximum points of the pseudo-spectrum,max{e _(τ) ^(H) {tilde over (R)} _(YY) e _(τ)}=max{trace({tilde over(R)} _(YY) e _(τ) e _(τ) ^(H))}  (9)

Searching the maxima of (8) is equivalent as searching the maxima of thequadratic form in the numerator e_(τ) ^(H){tilde over (R)}_(YY)e_(τ).Maximizing the numerator is equivalent to maximizing the trace of thematrix in the left-handed expression of (9). Note that the trace of amatrix is the sum of the elements of the diagonal of said.

Denoting E_(p)=e_(τ)e_(τ) ^(H) and ρ=e^(−jω) ⁰ ^(τ) the square-matrixE_(ρ) can be written as:

$\begin{matrix}{E_{\rho} = \begin{bmatrix}1 & \rho^{- 1} & \rho^{- 2} & \ldots & \rho^{- {({K - 1})}} \\\rho & 1 & \rho^{- 1} & \ldots & \rho^{- {({K - 2})}} \\\rho^{2} & \rho & 1 & \ldots & \rho^{- {({K - 3})}} \\\vdots & \vdots & \vdots & \ddots & \vdots \\\rho^{({K - 1})} & \rho^{({K - 2})} & \ldots & \rho & 1\end{bmatrix}} & (10)\end{matrix}$and the trace can be expressed in terms of the following polynomial,

$\begin{matrix}{{{trace}\left( {{\overset{\sim}{R}}_{YY}E_{\rho}} \right)} = {\sum\limits_{l = 0}^{K - 1}{\sum\limits_{k = 0}^{K - 1}{R_{k \cdot l}\rho^{({k - l})}}}}} & (11)\end{matrix}$where R_(k,1) denotes the k-th row, l-th column element of thecorrelation matrix {tilde over (R)}_(YY).

The estimation problem is then reduced to finding the roots whichcorrespond to maxima (by evaluating them in the second derivative) ofthe following polynomial

$\begin{matrix}{{\sum\limits_{k = {1 - K}}^{K - 1}{{kD}_{k}\rho^{k}}} = 0} & (12)\end{matrix}$where

$D_{k} = {\sum\limits_{i = 1}^{K}R_{i - {k \cdot l}}}$is defined as the addition of the elements of the n-th diagonal of thecorrelation matrix {tilde over (R)}_(YY). The coefficients in thepolynomial (12) are calculated by summing the elements of the k-diagonalof the matrix {tilde over (R)}_(YY).

In summary, the present invention provides a low complexity method forthe time-of-arrival (ToA) estimation of a signal transmitted through awireless system. The method is based on a frequency domain approach,which allows sub-Nyquist sampling rates while to achieving high(centimetre, depends on the implementation) ranging accuracy. Themotivation to consider a frequency domain approach is, as already shown,two fold: to allow for lower complexity implementation requirementsassociated to the receiver architecture and to enable accurate rangingestimation, which can potentially be implemented using high resolutionspectral estimation algorithms. Given the inherent high time resolutionof the UWB signal, we have considered simpler techniques, such as theperiodogram.

The invention is obviously not limited to the specific embodimentsdescribed herein, but also encompasses any variations that may beconsidered by any person skilled in the art (for example, as regards thechoice of components, configuration, etc.), within the general scope ofthe invention as defined in the appended claims.

1. A method for estimating a time-of-arrival of a received signal y(t), the method comprising the steps of: generating a plurality of frequency-domain samples (Y(0), Y(1), . . . , Y(K−1) from the received signal y(t); estimating a correlation matrix {tilde over (R)}_(YY) from the plurality of frequency-domain samples; calculating a signal energy distribution with respect to different propagation delays from the correlation matrix {tilde over (R)}_(YY); and finding a delay value ({tilde over (τ)}₀) at which the signal energy distribution exceeds a certain threshold P_(th), the delay value ({tilde over (τ)}₀) representing the time-of-arrival estimation; wherein the signal energy distribution is given by a computation of a pseudo-periodogram; wherein the pseudo-periodogram takes the form of P _(n)(τ)=e _(τ) ^(H) {tilde over (R)} _(YY)(n)e _(τ) wherein {tilde over (R)}_(YY)(n) is the previously estimated correlation matrix of the sampled signal in the frequency domain corresponding to an n-th sample interval, e_(τ)=[1e^(−jω) ⁰ ^(τ) . . . e^(−jω) ⁰ ^((K−1)τ)]^(T) is a delay-signature vector, and wherein ω₀=2 π/K, τ is the temporal delay and K is the number of frequency samples at each observation vector.
 2. The method of claim 1, wherein the step of estimating a correlation matrix {tilde over (R)}_(YY) is performed by calculating ${{\overset{\sim}{R}}_{YY}(n)} = {\frac{1}{N_{s}}{\sum\limits_{s = 1}^{N_{s}}{Y_{s,n}Y_{s,n}^{H}}}}$ wherein n denotes the n-th sampling interval, N_(s) is the number of realizations observed, and Y_(s,n)=[Y_(s,n)(0)Y_(s,n)(1) . . . Y_(s,n)(K−1)]^(T) are the K frequency components of the observation vector at realization s and sample interval n.
 3. The method of claim 1, wherein the received signal y(t) is an ultra-wideband signal.
 4. The method of claim 3, wherein the ultra-wideband signal is an impulse radio ultra-wideband signal.
 5. The method of claim 4, wherein the step of estimating a correlation matrix {tilde over (R)}_(YY) from a plurality of frequency-domain samples is performed by exploiting a temporal diversity of the impulse radio ultra-wideband signal.
 6. The method of claim 5, wherein the step of estimating a correlation matrix {tilde over (R)}_(YY) is performed by calculating ${{\overset{\sim}{R}}_{YY}(n)} = {\frac{1}{N_{s}}{\sum\limits_{s = 1}^{N_{s}}{Z_{s,n}Z_{s,n}^{H}}}}$ wherein n denotes the n-th sampling interval, N_(s) is the number of realizations observed, Z_(s,n)=[Y_(s,n) ⁽¹⁾ . . . Y_(s,n) ^((N) ^(p) ⁾] is a diversity matrix, wherein N_(p) is the number of repeated pulses transmitted, the elements of Y_(s,n) ^((p))are the frequency components associated to received pulse p at realization s and sample interval n, wherein p is a natural number which goes from 1 to N_(p).
 7. A method for estimating a time-of-arrival of a received signal y(t), the method comprising the steps of: generating a plurality of frequency-domain samples (Y(0), Y(1), . . . , Y(K−1)) from the received signal y(t); estimating a correlation matrix {tilde over (R)}_(YY) from the plurality of frequency-domain samples; calculating a signal energy distribution with respect to different propagation delays from the correlation matrix {tilde over (R)}_(YY); and finding a delay value ({tilde over (τ)}₀)at which the signal energy distribution exceeds a certain threshold P_(th), the delay value ({tilde over (τ)}₀)representing the time-of-arrival estimation; wherein the step of finding the delay value ({tilde over (τ)}₀) is performed by calculating the roots of a polynomial: wherein the polynomial takes the form of ${\sum\limits_{k = {1 - K}}^{K - 1}{{kD}_{k}\rho^{k}}} = 0$ where $D_{k} = {\sum\limits_{l = 1}^{K}R_{{l - k},l}}$  is the addition of the elements of the n-th diagonal of the correlation matrix {tilde over (R)}_(YY) and ρ=e^(−jω) ⁰ ^(τ), wherein ^(ω) ⁰ =2π/K, and ^(τ) is the temporal delay.
 8. The method of claim 7, wherein the signal energy distribution is given by a computation of a pseudo-periodogram; wherein the pseudo-periodogram takes form of P _(n)(τ)=e_(τ) ^(H){tilde over (R)}_(YY)(n)e_(τ) wherein {tilde over (R)}_(YY)(n) is the previously estimated correlation matrix of the sampled signal in the frequency domain corresponding to an n-th sample interval, e_(τ=[)1e^(−jω) ⁰ ^(τ) . . . e^(−jω) ⁰ ^((K−1)τ)]^(T) is a delay-signature vector, and wherein ω₀=2π/K, τ is the temporal delay and K is the number of frequency samples at each observation vector.
 9. The method of claim 7, wherein the received signal y(t) is an ultra-wideband signal.
 10. The method of claim 9, wherein the ultra-wideband signal is an impulse radio ultra-wideband signal.
 11. The method of claim 10, wherein the step of estimating a correlation matrix {tilde over (R)}_(YY) from a plurality of frequency-domain samples is performed by exploiting a temporal diversity of the impulse radio ultra-wideband signal.
 12. The method of claim 11, wherein the step of estimating a correlation matrix {tilde over (R)}_(YY) is performed by calculating ${{\overset{\sim}{R}}_{YY}(n)} = {\frac{1}{N_{s}}{\sum\limits_{s = 1}^{N_{s}}{Z_{s,n}Z_{s,n}^{H}}}}$ wherein n denotes the n-th sampling interval, N_(s) is the number of realizations observed, Z_(s,n)=[Y_(s,n) ⁽¹⁾ . . . Y_(s,n) ^((N) ^(p) ⁾] is a diversity matrix, wherein N_(p)is the number of repeated pulses transmitted, the elements of Y_(s,n) ^((p))are the frequency components associated to received pulse p at realization s and sample interval n, wherein p is a natural number which goes from 1 to N_(p).
 13. The method of claim 7, wherein the step of estimating a correlation matrix {tilde over (R)}_(YY) is performed by calculating ${{\overset{\sim}{R}}_{YY}(n)} = {\frac{1}{N_{s}}{\sum\limits_{s = 1}^{N_{s}}{Y_{s,n}Y_{s,n}^{H}}}}$ wherein n denotes the n-th sampling interval, N_(s) is the number of realizations observed, and Y_(s,n)=[Y_(s,n)(0)Y_(s,n)(1) . . . Y_(s,n)(K−1)]^(T) are the K frequency components of the observation vector at realization s and sample interval n.
 14. A method for estimating a time-of-arrival of a received signal y(t), the method comprising the steps of: generating a plurality of frequency-domain samples (Y(0), Y(1), . . . , Y(K−1)) from the received signal y(t); estimating a correlation matrix {tilde over (R)}_(YY) from the plurality of frequency-domain samples; calculating a signal enemy distribution with respect to different propagation delays from the correlation matrix {tilde over (R)}_(YY); and finding a delay value ({tilde over (τ)}₀) at which the signal energy distribution exceeds a certain threshold P_(th), the delay value ({tilde over (τ)}₀)representing the time-of-arrival estimation; wherein the step of generating a plurality of frequency-domain samples (Y(0), Y(1), . . . , Y(K−1)) from the received signal y(t) is performed by splitting the received signal y(t) into a plurality of bands by filtering the received signal by band-pass filters (25-1, . . . , 25-N) with approximately Gaussian frequency response; sampling (28-1, . . . , 28-N) the output of each of the band-pass filters thereby obtaining a plurality of samples (S(0), S(1), . . . , S(N−1)); from the plurality of samples (S(0), S(1), . . . , S(N−1)), building a vector S such that S=[S(0)S(1) . . . S(N−1)]; from the vector S, creating a vector S′ such that S′=[S(N−1)S(N−2) . . . S(0)]; and creating a vector Y which is the concatenation of vector S, a vector of zeros of size Q, where Q≧1 and vector S′.
 15. Method according to claim 14, wherein vector Y further comprises at least one element equal to zero at each of the extremes of the vector Y.
 16. The method of claim 14, wherein the signal energy distribution is given by a computation of a pseudo-periodogram; wherein the pseudo-periodogram takes form of P _(n)(τ)=e _(τ) ^(H){tilde over (R)}_(YY)(n)e _(τ) wherein {tilde over (R)}_(YY)(n) is the previously estimated correlation matrix of the sampled signal in the frequency domain corresponding to an n-th sample interval, e_(τ=[)1e^(−jω) ⁰ ^(τ) . . . e^(−jω) ⁰ ^((K−1)τ)]^(T) is a delay-signature vector, and wherein ω₀=2π/K, τ is the temporal delay and K is the number of frequency samples at each observation vector.
 17. The method of claim 14, wherein the received signal y(t) is an ultra-wideband signal.
 18. The method of claim 17, wherein the ultra-wideband signal is an impulse radio ultra-wideband signal.
 19. The method of claim 18, wherein the step of estimating a correlation matrix {tilde over (R)}_(YY) is performed by calculating ${{\overset{\sim}{R}}_{YY}(n)} = {\frac{1}{N_{s}}{\sum\limits_{s = 1}^{N_{s}}{Z_{s,n}Z_{s,n}^{H}}}}$ wherein n denotes the n-th sampling interval, N_(s) is the number of realizations observed, Z_(s,n)=[Y_(s,n) ⁽¹⁾ . . . Y_(s,n) ^((N) ^(p) ⁾] is a diversity matrix, wherein N_(p) is the number of repeated pulses transmitted, the elements of Y_(s,n) ^((p)) are the frequency components associated to received pulse p at realization s and sample interval n, wherein p is a natural number which goes from 1 to N_(p).
 20. The method of claim 14, wherein the step of estimating a correlation matrix {tilde over (R)}_(YY) is performed by calculating ${{\overset{\sim}{R}}_{YY}(n)} = {\frac{1}{N_{s}}{\sum\limits_{s = 1}^{N_{s}}{Y_{s,n}Y_{s,n}^{H}}}}$ wherein n denotes the n-th sampling interval, N_(s) is the number of realizations observed, and Y_(s,n)=[Y_(s,n)(0)Y_(s,n)(1) . . . Y_(s,n)(K−1)]^(T) are the K frequency components of the observation vector at realization s and sample interval n. 